The effect of weak inertia on flow through a porous medium

Mei, Chiang C.; Auriault, Jean‐Louis

doi:10.1017/s0022112091001258

Cited by 259 publications

(196 citation statements)

References 18 publications

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“…The multiple-scales technique that we exploit has been widely employed in homogenization of flow and transport in porous media in Keller (1980), Mei and Auriault (1991), Rubinstein (1987), and Tartar (1980), and more recently to simple models of growing tissue in O'Dea et al (2014) and Penta et al (2014) -here we seek to extend these ideas to a more complex description of the underlying tissue dynamics, incorporating multiple phases as well as microstructural features. We obtain a tissue-scale description of tumour growth and response, and transport of drug and nutrient comprising a system of advection-reaction PDEs that are partially parameterized by the solution to a tensor Stokes problem on a microscopic periodic unit.…”

Section: Discussionmentioning

confidence: 99%

“…There is an extensive literature related to the classical homogenization of flow and transport in porous media in both physical and biological applications, see, e.g. Keller (1980), Mei and Auriault (1991), Rubinstein (1987), and Tartar (1980). The analysis we present here represents an extension of the traditional homogenization of flow and transport phenomena and the recent attempts to apply these ideas to growing material in O'Dea et al…”

Section: Model Descriptionmentioning

confidence: 99%

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A multi-scale analysis of drug transport and response for a multi-phase tumour model

2016

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In this article we consider the spatial homogenization of a multiphase model for avascular tumour growth and response to chemotherapeutic treatment. The key contribution of this work is the derivation of a system of homogenized partial differential equations describing macroscopic tumour growth, coupled to transport of drug and nutrient, that explicitly incorporates details of the structure and dynamics of the tumour at the microscale. In order to derive these equations we employ an asymptotic homogenization of a microscopic description under the assumption of strong interphase drag, periodic microstructure, and strong separation of scales. The resulting macroscale model comprises a Darcy flow coupled to a system of reaction-advection partial differential equations. The coupled growth, response, and transport dynamics on the tissue scale are investigated via numerical experiments for simple academic test cases of microstructural information and tissue geometry, in which we observe drug-and nutrient-regulated growth and response consistent with the anticipated dynamics of the macroscale system.

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Section: Discussionmentioning

confidence: 99%

Section: Model Descriptionmentioning

confidence: 99%

A multi-scale analysis of drug transport and response for a multi-phase tumour model

2016

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“…This law was first shown numerically (Barrére, 1990) and then derived theoretically for homogeneous isotropic media (Mei and Auriault, 1991).…”

Section: Cherubini Et Al: Bench Scale Laboratory Tests To Analyzementioning

confidence: 96%

Bench scale laboratory tests to analyze non-linear flow in fractured media

Cherubini

Giasi

Pastore

2012

Hydrol. Earth Syst. Sci.

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Abstract. The knowledge of flow phenomena in fractured rocks is very important for groundwater resources management in hydrogeological engineering.A critical emerging issue for fractured aquifers is the validity of the Darcian-type "local cubic law", which assumes a linear relationship between flow rate and pressure gradient to accurately describe flow patterns.Experimental data obtained under controlled conditions such as in a laboratory increase our understanding of the fundamental physics of fracture flow and allow us to investigate the presence of non-linear flow inside fractures that generates a substantial deviation from Darcy's law.In this study the presence of non-linear flow in a fractured rock formation has been analyzed at bench scale in laboratory tests. The effects of non-linearity in flow have been investigated by analyzing hydraulic tests on an artificially created fractured rock sample of parallelepiped (0.60 × 0.40 × 0.8 m) shape.The volumes of water passing through different paths across the fractured sample for various hydraulic head differences have been measured, and the results of the experiments have been reported as specific flow rate vs. head gradient. The experimental results closely match the Forchheimer equation and describe a strong inertial regime. The results of the test have been interpreted by means of numerical simulations. For each pair of ports, several steady-state simulations have been carried out varying the hydraulic head difference between the inlet and outlet ports. The estimated linear and non-linear Forchheimer coefficients have been correlated to each other and respectively to the tortuosity of the flow paths.A correlation among the linear and non-linear Forchheimer coefficients is evident. Moreover, a tortuosity factor that influences flow dynamics has been determined.

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“…Global parameters can also be derived through modelling from first principles as, for instance, described in Lee and Howell (1987), Kuwahara et al (1998) and Pedras and Lemos (2000). In Mei and Auriault (1991), theoretical analysis yields that if inertia is weak, inertia is more important locally than globally and in other studies the validity of Forchheimer equation is investigated by mathematical derivations based on first principles, e.g. Skjetne and Auriault (1999), Adler et al (2013) and Soulaine and Quintard (2014).…”

Section: Introductionmentioning

confidence: 99%

Transitional and Turbulent Flow in a Bed of Spheres as Measured with Stereoscopic Particle Image Velocimetry

et al. 2017

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Stereoscopic particle image velocimetry has been used to investigate inertia dominated, transitional and turbulent flow in a randomly packed bed of monosized PMMA spheres. By using an index-matched fluid, the bed is optically transparent and measurements can be performed in an arbitrary position within the porous bed. The velocity field observations are carried out for particle Reynolds numbers, Re p , between 20 and 3220, and the sampling is done at a frequency of 75 Hz. Results show that, in porous media, the dynamics of the flow can vary significantly from pore to pore. At Re p around 400 the spatially averaged time fluctuations of total velocity reach a maximum and the spatial variation of the time-averaged total velocity, u tot increases up to about the same Re p and then it decreases. Also in the studied planes, a considerable amount of the fluid moves in the perpendicular directions to the main flow direction and the time-averaged magnitude of the velocity in the main direction, u x , has an averaged minimum of 40% of the magnitude of u tot at Re p about 400. For Re p > 1600, this ratio is nearly constant and u x is on average a little bit less than 50% of u tot . The importance of the results for longitudinal and transverse dispersion is discussed.

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The effect of weak inertia on flow through a porous medium

Cited by 259 publications

References 18 publications

A multi-scale analysis of drug transport and response for a multi-phase tumour model

A multi-scale analysis of drug transport and response for a multi-phase tumour model

Bench scale laboratory tests to analyze non-linear flow in fractured media

Transitional and Turbulent Flow in a Bed of Spheres as Measured with Stereoscopic Particle Image Velocimetry

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